/* return P(X + c) using destructive Horner, optimize for c = 1,-1 */
GEN
translate_pol(GEN P, GEN c)
{
pari_sp av = avma, lim;
GEN Q, *R;
long i, k, n;
if (!signe(P) || gcmp0(c)) return gcopy(P);
Q = shallowcopy(P);
R = (GEN*)(Q+2); n = degpol(P);
lim = stack_lim(av, 2);
if (gcmp1(c))
{
for (i=1; i<=n; i++)
{
for (k=n-i; k<n; k++) R[k] = gadd(R[k], R[k+1]);
if (low_stack(lim, stack_lim(av,2)))
{
if(DEBUGMEM>1) pari_warn(warnmem,"TR_POL(1), i = %ld/%ld", i,n);
Q = gerepilecopy(av, Q); R = (GEN*)Q+2;
}
}
}
else if (gcmp_1(c))
{
for (i=1; i<=n; i++)
{
for (k=n-i; k<n; k++) R[k] = gsub(R[k], R[k+1]);
if (low_stack(lim, stack_lim(av,2)))
{
if(DEBUGMEM>1) pari_warn(warnmem,"TR_POL(-1), i = %ld/%ld", i,n);
Q = gerepilecopy(av, Q); R = (GEN*)Q+2;
}
}
}
else
{
for (i=1; i<=n; i++)
{
for (k=n-i; k<n; k++) R[k] = gadd(R[k], gmul(c, R[k+1]));
if (low_stack(lim, stack_lim(av,2)))
{
if(DEBUGMEM>1) pari_warn(warnmem,"TR_POL, i = %ld/%ld", i,n);
Q = gerepilecopy(av, Q); R = (GEN*)Q+2;
}
}
}
return gerepilecopy(av, Q);
}
// Digit reversal
GEN
rev(GEN n, long B)
{
pari_sp av = avma;
if (typ(n) != t_INT)
pari_err_TYPE("rev", n);
GEN m = modis(n, B);
n = divis(n, B);
pari_sp btop = avma, st_lim = stack_lim(btop, 1);
while (signe(n)) {
m = addis(mulis(m, B), smodis(n, B));
n = divis(n, B);
if (low_stack(st_lim, stack_lim(btop, 1)))
gerepileall(btop, 2, &m, &n);
}
m = gerepilecopy(av, m);
return m;
}
int
ratlift(GEN x, GEN m, GEN *a, GEN *b, GEN amax, GEN bmax)
{
GEN d,d1,v,v1,q,r;
pari_sp av = avma, av1, lim;
long lb,lr,lbb,lbr,s,s0;
ulong vmax;
ulong xu,xu1,xv,xv1; /* Lehmer stage recurrence matrix */
int lhmres; /* Lehmer stage return value */
if ((typ(x) | typ(m) | typ(amax) | typ(bmax)) != t_INT) pari_err(arither1);
if (signe(bmax) <= 0)
pari_err(talker, "ratlift: bmax must be > 0, found\n\tbmax=%Z\n", bmax);
if (signe(amax) < 0)
pari_err(talker, "ratilft: amax must be >= 0, found\n\tamax=%Z\n", amax);
/* check 2*amax*bmax < m */
if (cmpii(shifti(mulii(amax, bmax), 1), m) >= 0)
pari_err(talker, "ratlift: must have 2*amax*bmax < m, found\n\tamax=%Z\n\tbmax=%Z\n\tm=%Z\n", amax,bmax,m);
/* we _could_ silently replace x with modii(x,m) instead of the following,
* but let's leave this up to the caller
*/
avma = av; s = signe(x);
if (s < 0 || cmpii(x,m) >= 0)
pari_err(talker, "ratlift: must have 0 <= x < m, found\n\tx=%Z\n\tm=%Z\n", x,m);
/* special cases x=0 and/or amax=0 */
if (s == 0)
{
if (a != NULL) *a = gen_0;
if (b != NULL) *b = gen_1;
return 1;
}
else if (signe(amax)==0)
return 0;
/* assert: m > x > 0, amax > 0 */
/* check here whether a=x, b=1 is a solution */
if (cmpii(x,amax) <= 0)
{
if (a != NULL) *a = icopy(x);
if (b != NULL) *b = gen_1;
return 1;
}
/* There is no special case for single-word numbers since this is
* mainly meant to be used with large moduli.
*/
(void)new_chunk(lgefint(bmax) + lgefint(amax)); /* room for a,b */
d = m; d1 = x;
v = gen_0; v1 = gen_1;
/* assert d1 > amax, v1 <= bmax here */
lb = lgefint(bmax);
lbb = bfffo(*int_MSW(bmax));
s = 1;
av1 = avma; lim = stack_lim(av, 1);
/* general case: Euclidean division chain starting with m div x, and
* with bounds on the sequence of convergents' denoms v_j.
* Just to be different from what invmod and bezout are doing, we work
* here with the all-nonnegative matrices [u,u1;v,v1]=prod_j([0,1;1,q_j]).
* Loop invariants:
* (a) (sign)*[-v,v1]*x = [d,d1] (mod m) (componentwise)
* (sign initially +1, changes with each Euclidean step)
* so [a,b] will be obtained in the form [-+d,v] or [+-d1,v1];
* this congruence is a consequence of
* (b) [x,m]~ = [u,u1;v,v1]*[d1,d]~,
* where u,u1 is the usual numerator sequence starting with 1,0
* instead of 0,1 (just multiply the eqn on the left by the inverse
* matrix, which is det*[v1,-u1;-v,u], where "det" is the same as the
* "(sign)" in (a)). From m = v*d1 + v1*d and
* (c) d > d1 >= 0, 0 <= v < v1,
* we have d >= m/(2*v1), so while v1 remains smaller than m/(2*amax),
* the pair [-(sign)*d,v] satisfies (1) but violates (2) (d > amax).
* Conversely, v1 > bmax indicates that no further solutions will be
* forthcoming; [-(sign)*d,v] will be the last, and first, candidate.
* Thus there's at most one point in the chain division where a solution
* can live: v < bmax, v1 >= m/(2*amax) > bmax, and this is acceptable
* iff in fact d <= amax (e.g. m=221, x=34 or 35, amax=bmax=10 fail on
* this count while x=32,33,36,37 succeed). However, a division may leave
* a zero residue before we ever reach this point (consider m=210, x=35,
* amax=bmax=10), and our caller may find that gcd(d,v) > 1 (numerous
* examples -- keep m=210 and consider any of x=29,31,32,33,34,36,37,38,
* 39,40,41).
* Furthermore, at the start of the loop body we have in fact
* (c') 0 <= v < v1 <= bmax, d > d1 > amax >= 0,
* (and are never done already).
*
* Main loop is similar to those of invmod() and bezout(), except for
* having to determine appropriate vmax bounds, and checking termination
* conditions. The signe(d1) condition is only for paranoia
*/
while (lgefint(d) > 3 && signe(d1))
{
/* determine vmax for lgcdii so as to ensure v won't overshoot.
* If v+v1 > bmax, the next step would take v1 beyond the limit, so
* since [+-d1,v1] is not a solution, we give up. Otherwise if v+v1
* is way shorter than bmax, use vmax=MAXULUNG. Otherwise, set vmax
* to a crude lower approximation of bmax/(v+v1), or to 1, which will
* allow the inner loop to do one step
*/
r = addii(v,v1);
lr = lb - lgefint(r);
lbr = bfffo(*int_MSW(r));
if (cmpii(r,bmax) > 0) /* done, not found */
{
avma = av;
return 0;
}
else if (lr > 1) /* still more than a word's worth to go */
{
vmax = MAXULONG;
}
else /* take difference of bit lengths */
{
lr = (lr << TWOPOTBITS_IN_LONG) - lbb + lbr;
if ((ulong)lr > BITS_IN_LONG)
vmax = MAXULONG;
else if (lr == 0)
vmax = 1UL;
else
vmax = 1UL << (lr-1);
/* the latter is pessimistic but faster than a division */
}
/* do a Lehmer-Jebelean round */
lhmres = lgcdii((ulong *)d, (ulong *)d1, &xu, &xu1, &xv, &xv1, vmax);
if (lhmres != 0) /* check progress */
{ /* apply matrix */
if ((lhmres == 1) || (lhmres == -1))
{
s = -s;
if (xv1 == 1)
{
/* re-use v+v1 computed above */
v=v1; v1=r;
r = subii(d,d1); d=d1; d1=r;
}
else
{
r = subii(d, mului(xv1,d1)); d=d1; d1=r;
r = addii(v, mului(xv1,v1)); v=v1; v1=r;
}
}
else
{
r = subii(muliu(d,xu), muliu(d1,xv));
d1 = subii(muliu(d,xu1), muliu(d1,xv1)); d = r;
r = addii(muliu(v,xu), muliu(v1,xv));
v1 = addii(muliu(v,xu1), muliu(v1,xv1)); v = r;
if (lhmres&1)
{
setsigne(d,-signe(d));
s = -s;
}
else if (signe(d1))
{
setsigne(d1,-signe(d1));
}
}
/* check whether we're done. Assert v <= bmax here. Examine v1:
* if v1 > bmax, check d and return 0 or 1 depending on the outcome;
* if v1 <= bmax, check d1 and return 1 if d1 <= amax, otherwise
* proceed.
*/
if (cmpii(v1,bmax) > 0) /* certainly done */
{
avma = av;
if (cmpii(d,amax) <= 0) /* done, found */
{
if (a != NULL)
{
*a = icopy(d);
setsigne(*a,-s); /* sign opposite to s */
}
if (b != NULL) *b = icopy(v);
return 1;
}
else /* done, not found */
return 0;
}
else if (cmpii(d1,amax) <= 0) /* also done, found */
{
avma = av;
if (a != NULL)
{
if (signe(d1))
{
*a = icopy(d1);
setsigne(*a,s); /* same sign as s */
}
else
*a = gen_0;
}
if (b != NULL) *b = icopy(v1);
return 1;
}
} /* lhmres != 0 */
if (lhmres <= 0 && signe(d1))
{
q = dvmdii(d,d1,&r);
#ifdef DEBUG_LEHMER
fprintferr("Full division:\n");
printf(" q = "); output(q); sleep (1);
#endif
d=d1; d1=r;
r = addii(v,mulii(q,v1));
v=v1; v1=r;
s = -s;
/* check whether we are done now. Since we weren't before the div, it
* suffices to examine v1 and d1 -- the new d (former d1) cannot cut it
*/
if (cmpii(v1,bmax) > 0) /* done, not found */
{
avma = av;
return 0;
}
else if (cmpii(d1,amax) <= 0) /* done, found */
{
avma = av;
if (a != NULL)
{
if (signe(d1))
{
*a = icopy(d1);
setsigne(*a,s); /* same sign as s */
}
else
*a = gen_0;
}
if (b != NULL) *b = icopy(v1);
return 1;
}
}
if (low_stack(lim, stack_lim(av,1)))
{
GEN *gptr[4]; gptr[0]=&d; gptr[1]=&d1; gptr[2]=&v; gptr[3]=&v1;
if(DEBUGMEM>1) pari_warn(warnmem,"ratlift");
gerepilemany(av1,gptr,4);
}
} /* end while */
/* Postprocessing - final sprint. Since we usually underestimate vmax,
* this function needs a loop here instead of a simple conditional.
* Note we can only get here when amax fits into one word (which will
* typically not be the case!). The condition is bogus -- d1 is never
* zero at the start of the loop. There will be at most a few iterations,
* so we don't bother collecting garbage
*/
while (signe(d1))
{
/* Assertions: lgefint(d)==lgefint(d1)==3.
* Moreover, we aren't done already, or we would have returned by now.
* Recompute vmax...
*/
#ifdef DEBUG_RATLIFT
fprintferr("rl-fs: d,d1=%Z,%Z\n", d, d1);
fprintferr("rl-fs: v,v1=%Z,%Z\n", v, v1);
#endif
r = addii(v,v1);
lr = lb - lgefint(r);
lbr = bfffo(*int_MSW(r));
if (cmpii(r,bmax) > 0) /* done, not found */
{
avma = av;
return 0;
}
else if (lr > 1) /* still more than a word's worth to go */
{
vmax = MAXULONG; /* (cannot in fact happen) */
}
else /* take difference of bit lengths */
{
lr = (lr << TWOPOTBITS_IN_LONG) - lbb + lbr;
if ((ulong)lr > BITS_IN_LONG)
vmax = MAXULONG;
else if (lr == 0)
vmax = 1UL;
else
vmax = 1UL << (lr-1); /* as above */
}
#ifdef DEBUG_RATLIFT
fprintferr("rl-fs: vmax=%lu\n", vmax);
#endif
/* single-word "Lehmer", discarding the gcd or whatever it returns */
(void)rgcduu((ulong)*int_MSW(d), (ulong)*int_MSW(d1), vmax, &xu, &xu1, &xv, &xv1, &s0);
#ifdef DEBUG_RATLIFT
fprintferr("rl-fs: [%lu,%lu; %lu,%lu] %s\n",
xu, xu1, xv, xv1,
s0 < 0 ? "-" : "+");
#endif
if (xv1 == 1) /* avoid multiplications */
{
/* re-use v+v1 computed above */
v=v1; v1=r;
r = subii(d,d1); d=d1; d1=r;
s = -s;
}
else if (xu == 0) /* and xv==1, xu1==1, xv1 > 1 */
{
r = subii(d, mului(xv1,d1)); d=d1; d1=r;
r = addii(v, mului(xv1,v1)); v=v1; v1=r;
s = -s;
}
else
{
r = subii(muliu(d,xu), muliu(d1,xv));
d1 = subii(muliu(d,xu1), muliu(d1,xv1)); d = r;
r = addii(muliu(v,xu), muliu(v1,xv));
v1 = addii(muliu(v,xu1), muliu(v1,xv1)); v = r;
if (s0 < 0)
{
setsigne(d,-signe(d));
s = -s;
}
else if (signe(d1)) /* sic: might vanish now */
{
setsigne(d1,-signe(d1));
}
}
/* check whether we're done, as above. Assert v <= bmax. Examine v1:
* if v1 > bmax, check d and return 0 or 1 depending on the outcome;
* if v1 <= bmax, check d1 and return 1 if d1 <= amax, otherwise proceed.
*/
if (cmpii(v1,bmax) > 0) /* certainly done */
{
avma = av;
if (cmpii(d,amax) <= 0) /* done, found */
{
if (a != NULL)
{
*a = icopy(d);
setsigne(*a,-s); /* sign opposite to s */
}
if (b != NULL) *b = icopy(v);
return 1;
}
else /* done, not found */
return 0;
}
else if (cmpii(d1,amax) <= 0) /* also done, found */
{
avma = av;
if (a != NULL)
{
if (signe(d1))
{
*a = icopy(d1);
setsigne(*a,s); /* same sign as s */
}
else
*a = gen_0;
}
if (b != NULL) *b = icopy(v1);
return 1;
}
} /* while */
/* get here when we have run into d1 == 0 before returning... in fact,
* this cannot happen.
*/
pari_err(talker, "ratlift failed to catch d1 == 0\n");
/* NOTREACHED */
return 0;
}
static GEN
nf_LLL_cmbf(nfcmbf_t *T, GEN p, long k, long rec)
{
nflift_t *L = T->L;
GEN pk = L->pk, PRK = L->prk, PRKinv = L->iprk, GSmin = L->GSmin;
GEN Tpk = L->Tpk;
GEN famod = T->fact, nf = T->nf, ZC = T->ZC, Br = T->Br;
GEN Pbase = T->polbase, P = T->pol, dn = T->dn;
GEN nfT = gel(nf,1);
GEN Btra;
long dnf = degpol(nfT), dP = degpol(P);
double BitPerFactor = 0.5; /* nb bits / modular factor */
long i, C, tmax, n0;
GEN lP, Bnorm, Tra, T2, TT, CM_L, m, list, ZERO;
double Bhigh;
pari_sp av, av2, lim;
long ti_LLL = 0, ti_CF = 0;
pari_timer ti2, TI;
lP = absi(leading_term(P));
if (is_pm1(lP)) lP = NULL;
n0 = lg(famod) - 1;
/* Lattice: (S PRK), small vector (vS vP). To find k bound for the image,
* write S = S1 q + S0, P = P1 q + P0
* |S1 vS + P1 vP|^2 <= Bhigh for all (vS,vP) assoc. to true factors */
Btra = mulrr(ZC, mulsr(dP*dP, normlp(Br, 2, dnf)));
Bhigh = get_Bhigh(n0, dnf);
C = (long)ceil(sqrt(Bhigh/n0)) + 1; /* C^2 n0 ~ Bhigh */
Bnorm = dbltor( n0 * C * C + Bhigh );
ZERO = zeromat(n0, dnf);
av = avma; lim = stack_lim(av, 1);
TT = cgetg(n0+1, t_VEC);
Tra = cgetg(n0+1, t_MAT);
for (i=1; i<=n0; i++) TT[i] = 0;
CM_L = gscalsmat(C, n0);
/* tmax = current number of traces used (and computed so far) */
for(tmax = 0;; tmax++)
{
long a, b, bmin, bgood, delta, tnew = tmax + 1, r = lg(CM_L)-1;
GEN oldCM_L, M_L, q, S1, P1, VV;
int first = 1;
/* bound for f . S_k(genuine factor) = ZC * bound for T_2(S_tnew) */
Btra = mulrr(ZC, mulsr(dP*dP, normlp(Br, 2*tnew, dnf)));
bmin = logint(ceil_safe(sqrtr(Btra)), gen_2, NULL);
if (DEBUGLEVEL>2)
fprintferr("\nLLL_cmbf: %ld potential factors (tmax = %ld, bmin = %ld)\n",
r, tmax, bmin);
/* compute Newton sums (possibly relifting first) */
if (gcmp(GSmin, Btra) < 0)
{
nflift_t L1;
GEN polred;
bestlift_init(k<<1, nf, T->pr, Btra, &L1);
polred = ZqX_normalize(Pbase, lP, &L1);
k = L1.k;
pk = L1.pk;
PRK = L1.prk;
PRKinv = L1.iprk;
GSmin = L1.GSmin;
Tpk = L1.Tpk;
famod = hensel_lift_fact(polred, famod, Tpk, p, pk, k);
for (i=1; i<=n0; i++) TT[i] = 0;
}
for (i=1; i<=n0; i++)
{
GEN h, lPpow = lP? gpowgs(lP, tnew): NULL;
GEN z = polsym_gen(gel(famod,i), gel(TT,i), tnew, Tpk, pk);
gel(TT,i) = z;
h = gel(z,tnew+1);
/* make Newton sums integral */
lPpow = mul_content(lPpow, dn);
if (lPpow) h = FpX_red(gmul(h,lPpow), pk);
gel(Tra,i) = nf_bestlift(h, NULL, L); /* S_tnew(famod) */
}
/* compute truncation parameter */
if (DEBUGLEVEL>2) { TIMERstart(&ti2); TIMERstart(&TI); }
oldCM_L = CM_L;
av2 = avma;
b = delta = 0; /* -Wall */
AGAIN:
M_L = Q_div_to_int(CM_L, utoipos(C));
VV = get_V(Tra, M_L, PRK, PRKinv, pk, &a);
if (first)
{ /* initialize lattice, using few p-adic digits for traces */
bgood = (long)(a - max(32, BitPerFactor * r));
b = max(bmin, bgood);
delta = a - b;
}
else
{ /* add more p-adic digits and continue reduction */
if (a < b) b = a;
b = max(b-delta, bmin);
if (b - delta/2 < bmin) b = bmin; /* near there. Go all the way */
}
/* restart with truncated entries */
q = int2n(b);
P1 = gdivround(PRK, q);
S1 = gdivround(Tra, q);
T2 = gsub(gmul(S1, M_L), gmul(P1, VV));
m = vconcat( CM_L, T2 );
if (first)
{
first = 0;
m = shallowconcat( m, vconcat(ZERO, P1) );
/* [ C M_L 0 ]
* m = [ ] square matrix
* [ T2' PRK ] T2' = Tra * M_L truncated
*/
}
CM_L = LLL_check_progress(Bnorm, n0, m, b == bmin, /*dbg:*/ &ti_LLL);
if (DEBUGLEVEL>2)
fprintferr("LLL_cmbf: (a,b) =%4ld,%4ld; r =%3ld -->%3ld, time = %ld\n",
a,b, lg(m)-1, CM_L? lg(CM_L)-1: 1, TIMER(&TI));
if (!CM_L) { list = mkcol(QXQX_normalize(P,nfT)); break; }
if (b > bmin)
{
CM_L = gerepilecopy(av2, CM_L);
goto AGAIN;
}
if (DEBUGLEVEL>2) msgTIMER(&ti2, "for this trace");
i = lg(CM_L) - 1;
if (i == r && gequal(CM_L, oldCM_L))
{
CM_L = oldCM_L;
avma = av2; continue;
}
if (i <= r && i*rec < n0)
{
pari_timer ti;
if (DEBUGLEVEL>2) TIMERstart(&ti);
list = nf_chk_factors(T, P, Q_div_to_int(CM_L,utoipos(C)), famod, pk);
if (DEBUGLEVEL>2) ti_CF += TIMER(&ti);
if (list) break;
CM_L = gerepilecopy(av2, CM_L);
}
if (low_stack(lim, stack_lim(av,1)))
{
if(DEBUGMEM>1) pari_warn(warnmem,"nf_LLL_cmbf");
gerepileall(av, Tpk? 9: 8,
&CM_L,&TT,&Tra,&famod,&pk,&GSmin,&PRK,&PRKinv,&Tpk);
}
}
if (DEBUGLEVEL>2)
fprintferr("* Time LLL: %ld\n* Time Check Factor: %ld\n",ti_LLL,ti_CF);
return list;
}
int
invmod(GEN a, GEN b, GEN *res)
#endif
{
GEN v,v1,d,d1,q,r;
pari_sp av, av1, lim;
long s;
ulong g;
ulong xu,xu1,xv,xv1; /* Lehmer stage recurrence matrix */
int lhmres; /* Lehmer stage return value */
if (typ(a) != t_INT || typ(b) != t_INT) pari_err(arither1);
if (!signe(b)) { *res=absi(a); return 0; }
av = avma;
if (lgefint(b) == 3) /* single-word affair */
{
ulong d1 = umodiu(a, (ulong)(b[2]));
if (d1 == 0)
{
if (b[2] == 1L)
{ *res = gen_0; return 1; }
else
{ *res = absi(b); return 0; }
}
g = xgcduu((ulong)(b[2]), d1, 1, &xv, &xv1, &s);
#ifdef DEBUG_LEHMER
fprintferr(" <- %lu,%lu\n", (ulong)(b[2]), (ulong)(d1[2]));
fprintferr(" -> %lu,%ld,%lu; %lx\n", g,s,xv1,avma);
#endif
avma = av;
if (g != 1UL) { *res = utoipos(g); return 0; }
xv = xv1 % (ulong)(b[2]); if (s < 0) xv = ((ulong)(b[2])) - xv;
*res = utoipos(xv); return 1;
}
(void)new_chunk(lgefint(b));
d = absi(b); d1 = modii(a,d);
v=gen_0; v1=gen_1; /* general case */
#ifdef DEBUG_LEHMER
fprintferr("INVERT: -------------------------\n");
output(d1);
#endif
av1 = avma; lim = stack_lim(av,1);
while (lgefint(d) > 3 && signe(d1))
{
#ifdef DEBUG_LEHMER
fprintferr("Calling Lehmer:\n");
#endif
lhmres = lgcdii((ulong*)d, (ulong*)d1, &xu, &xu1, &xv, &xv1, MAXULONG);
if (lhmres != 0) /* check progress */
{ /* apply matrix */
#ifdef DEBUG_LEHMER
fprintferr("Lehmer returned %d [%lu,%lu;%lu,%lu].\n",
lhmres, xu, xu1, xv, xv1);
#endif
if ((lhmres == 1) || (lhmres == -1))
{
if (xv1 == 1)
{
r = subii(d,d1); d=d1; d1=r;
a = subii(v,v1); v=v1; v1=a;
}
else
{
r = subii(d, mului(xv1,d1)); d=d1; d1=r;
a = subii(v, mului(xv1,v1)); v=v1; v1=a;
}
}
else
{
r = subii(muliu(d,xu), muliu(d1,xv));
a = subii(muliu(v,xu), muliu(v1,xv));
d1 = subii(muliu(d,xu1), muliu(d1,xv1)); d = r;
v1 = subii(muliu(v,xu1), muliu(v1,xv1)); v = a;
if (lhmres&1)
{
setsigne(d,-signe(d));
setsigne(v,-signe(v));
}
else
{
if (signe(d1)) { setsigne(d1,-signe(d1)); }
setsigne(v1,-signe(v1));
}
}
}
#ifdef DEBUG_LEHMER
else
fprintferr("Lehmer returned 0.\n");
output(d); output(d1); output(v); output(v1);
sleep(1);
#endif
if (lhmres <= 0 && signe(d1))
{
q = dvmdii(d,d1,&r);
#ifdef DEBUG_LEHMER
fprintferr("Full division:\n");
printf(" q = "); output(q); sleep (1);
#endif
a = subii(v,mulii(q,v1));
v=v1; v1=a;
d=d1; d1=r;
}
if (low_stack(lim, stack_lim(av,1)))
{
GEN *gptr[4]; gptr[0]=&d; gptr[1]=&d1; gptr[2]=&v; gptr[3]=&v1;
if(DEBUGMEM>1) pari_warn(warnmem,"invmod");
gerepilemany(av1,gptr,4);
}
} /* end while */
/* Postprocessing - final sprint */
if (signe(d1))
{
/* Assertions: lgefint(d)==lgefint(d1)==3, and
* gcd(d,d1) is nonzero and fits into one word
*/
g = xxgcduu((ulong)d[2], (ulong)d1[2], 1, &xu, &xu1, &xv, &xv1, &s);
#ifdef DEBUG_LEHMER
output(d);output(d1);output(v);output(v1);
fprintferr(" <- %lu,%lu\n", (ulong)d[2], (ulong)d1[2]);
fprintferr(" -> %lu,%ld,%lu; %lx\n", g,s,xv1,avma);
#endif
if (g != 1UL) { avma = av; *res = utoipos(g); return 0; }
/* (From the xgcduu() blurb:)
* For finishing the multiword modinv, we now have to multiply the
* returned matrix (with properly adjusted signs) onto the values
* v' and v1' previously obtained from the multiword division steps.
* Actually, it is sufficient to take the scalar product of [v',v1']
* with [u1,-v1], and change the sign if s==1.
*/
v = subii(muliu(v,xu1),muliu(v1,xv1));
if (s > 0) setsigne(v,-signe(v));
avma = av; *res = modii(v,b);
#ifdef DEBUG_LEHMER
output(*res); fprintfderr("============================Done.\n");
sleep(1);
#endif
return 1;
}
/* get here when the final sprint was skipped (d1 was zero already) */
avma = av;
if (!equalii(d,gen_1)) { *res = icopy(d); return 0; }
*res = modii(v,b);
#ifdef DEBUG_LEHMER
output(*res); fprintferr("============================Done.\n");
sleep(1);
#endif
return 1;
}